Searches for transplutonian planets using long-period comets

We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.     

An intriguing correlation between the masses and periods of the transiting planets

We point out an intriguing relation between the masses of the transiting planets and their orbital periods. For the six currently known transiting planets, the data are consistent with a decreasing linear relation. The other known short-period planets, discovered through radial-velocity techniques, seem to agree with this relation. We briefly speculate about a tentative physical model to explain such a dependence.     

Parameterized post-Newtonian orbital effects in extrasolar planets

Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets.     

Global dynamics of the Gliese 876 planetary system

The Gliese 876 planetary system consists of two Jupiter-like planets having a nearly commensurate 2:1 orbital periods ratio. Because the semimajor axes of the planets are very small (of the order 0.1 au and 0.2 au, respectively), and the eccentricity of the inner companion is ≃0.3, the mutual perturbations are extremely large. However, many authors claim the long-term orbital stability of the system, at least over 500 Myr for initial conditions found by Rivera & Lissauer. Results of investigations of a migration of initially separated planets into the close 2:1 mean motion resonance lock from Lee & Peale also support the conclusion that the system should be stable for the lifetime of the parent star. Initial conditions of the system, found from non-linear N -body fits by Laughlin & Chambers and Rivera & Lissauer, to the radial velocity curve, formally allow for a variety of orbital configurations of the GJ 876 system, e.g. coplanar, with planetary inclinations in the range [≃30°, 90°], and with relative inclinations of orbital planes as high as 80°. Our work is devoted to the stability investigation of the systems originating from the fitted initial conditions. We study neighbourhoods of these initial states in the orbital parameter space. We found estimations of the 2:1 mean motion resonance width and dynamical limitations on the planetary masses. We also obtain a global representation of the domains of the orbital parameters space in which initial conditions leading to stable evolutions can be found. Our results can be useful in localization of the best, stable fits to the observational data. In our investigations we use the MEGNO technique (the Mean Exponential Growth factor of Nearby Orbits) invented by Cincotta & Simó. It allows us to distinguish efficiently and precisely between chaotic and regular behaviour of a planetary system.     

系外行星系统掩星周期变化研究进展

在掩星法发现的系外行星系统中,如果存在其他未知的伴星绕同一颗恒星运动,掩星行星由于受到伴星引力的影响,运动轨道将发生变化,轨道周期不再是常数,而是变化的。利用这种变化探测掩星系统中的其他行星,已成为一种新的方法。主要介绍了未知行星与掩星行星之间的引力作用引起的掩星周期变化效应,以及掩星周期变化法探测系外行星的理论和研究进展状况,最后简要讨论了几种影响掩星周期变化的其他因素:共轨行星、卫星、潮汐效应、相对论效应及恒星的引力四极矩等。     

Insolation patterns on synchronous exoplanets with obliquity

A previous paper [Dobrovolskis, A.R., 2007. Icarus 192, 1-23] showed that eccentricity can have profound effects on the climate, habitability, and detectability of extrasolar planets. This complementary study shows that obliquity can have comparable effects.The known exoplanets exhibit a wide range of orbital eccentricities, but those within several million kilometers of their suns are generally in near-circular orbits. This fact is widely attributed to the dissipation of tides in the planets. Tides in a planet affect its spin even more than its orbit, and such tidally evolved planets often are assumed to be in synchronous rotation, so that their rotation periods are identical to their orbital periods. The canonical example of synchronous spin is the way that our Moon always keeps nearly the same hemisphere facing the Earth.Tides also tend to reduce the planet’s obliquity (the angle between its spin and orbital angular velocities). However, orbit precession can cause the rotation to become locked in a “Cassini state”, where it retains a nearly constant non-zero obliquity. For example, our Moon maintains an obliquity of about 6.7° with respect to its orbit about the Earth. In comparison, stable Cassini states can exist for practically any obliquity up to ∼90° or more for planets of binary stars, or in multi-planet systems with high mutual inclinations, such as are produced by scattering or by the Kozai mechanism.This work considers planets in synchronous rotation with circular orbits, but arbitrary obliquity β; this affects the distribution of insolation over the planet’s surface, particularly near its poles. For β=0, one hemisphere bakes in perpetual sunshine, while the opposite hemisphere experiences eternal darkness. As β increases, the region of permanent daylight and the antipodal realm of endless night both shrink, while a more temperate area of alternating day and night spreads in longitude, and especially in latitude. The regions of permanent day or night disappear at β=90°. The insolation regime passes through several more transitions as β continues to increase toward 180°, but the surface distribution of insolation remains non-uniform in both latitude and longitude.Thus obliquity, like eccentricity, can protect certain areas of the planet from the worst extremes of temperature and solar radiation, and can improve the planet’s habitability. These results also have implications for the direct detectability of extrasolar planets, and for the interpretation of their thermal emissions.     

Resonances of low orders in the planetary system of HD37124

The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra Δω ~ 60°), whereas in the case of the 5/2 MMR it is a symmetric antialigned one (Δω = 180°). It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed 2.3 − 2.5.     

Identification of Asteroids in Two-Body Resonances

A catalog of asteroids in two-body orbital resonances with the planets of the Solar System has been created. The AstDyS database was a source of the input data, and all the numbered objects (467303 objects at the time of the analysis) were considered. The orbits were integrated in the framework of a pure gravitational problem considering all the planets of the Solar System and Pluto. From the analysis of the behavior of the resonant argument and the semimajor axis on the 100-kyr interval, the resonance membership and the libration type (pure or transient) were verified for each of the asteroids. A more accurate method to identify the resonant argument librations was developed on the basis of the analysis of mutual periodograms. We found 23251 resonant asteroids, ~36% of which (8397 objects) are in pure resonances.     

On the detection of mutual perturbations as proof of planets around PSR1257+12

Unambiguous detection of the consequences of mutual perturbations of the hypothesized planets about the pulsar PSR1257+12 would be unassailable proof of their existence. Nearly all of the residuals in the times of arrival (TOA) of the pulses after subtraction of the TOA predicted from the best fit constant period model are accounted for by including the effects of two orbiting planets with constant orbital parameters. The nature and magnitude of additional residuals in the TOA due to the gravitational interactions between the planets are determined by numerically calculating the TOA residuals for the orbital motion including the perturbations and subtracting the TOA residuals from analytic expressions of the orbital motion with orbital parameters fixed at averaged values. The TOA residual differences so obtained oscillate with periods comparable to the orbital periods with the oscillations varying in amplitude as a function of epoch within any given observational period. The signature of the perturbations is thus a quasiperiodic modulation of the residual differences obtained after removal of the effects of the orbital motion with best fit, constant orbital parameters. The amplitudes of this modulation reach about 10sec for observational periods exceeding 1000 days for the minimum planetary masses with sini = 1, and they increase as 1 / sini for 1 / sini < 5, wherei is the inclination of the orbit plane to that of the sky. Greater accumulated phase differences between the effects of perturbed and unperturbed orbital motions are available in the times of zero values in the observed and predicted TOA residuals and these comprise a second signature of the perturbations. The perturbation signatures should become detectable as the observation interval approaches 1000 days.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

太阳系外行星系统轨道参数的统计研究

自1995年第一颗类太阳恒星周围的系外行星发现以来,随着已发现的系外行星数目的增多,对系外行星性质的统计分析变得重要和有意义。截至2011年6月9日,共发现系外行星555颗。以这些系外行星的轨道参数为依据,对系外行星的性质进行统计分析,得出了一些有意义的结论。同时简要介绍现有的行星形成与演化模型并依据得出的行星统计性质对其进行检验,这对于系外行星的进一步探测具有一定的指导作用。     

Computer simulation of formation of terrestrial planets from planetesimals

A computer simulation of the accumulation of planetesimals into terrestrial planets is made on a model of the early solar system based on Refs. [1, 2]. The results show that, through the process of collisional coalescence, planetesimals gathered into a small number of large planets moving in nearly coplanar circular orbits. With suitable choice of the initial orbital elements and system parameters, results in general agreement with the actual system can be obtained.     

Giant planet migration through the action of disk torques and planet-planet scattering

This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.     

Prospects for spectroscopic reflected-light planet searches

High-resolution spectroscopic searches for the starlight reflected from close-in extrasolar giant planets have the capability of determining the optical albedo spectra and scattering properties of these objects. When combined with radial velocity measurements they also yield the true mass of the planet. To date, only two such planets have been targeted for reflected-light signals, yielding upper limits on the optical albedos of the planets. Here we examine the prospects for future searches of this kind. We present Monte Carlo estimates of prior probability distributions for the orbital velocity amplitudes and planet/star flux ratios of six bright stars known to harbour giant planets in orbits with periods of less than 5 d. Using these estimates, we assess the viability of these targets for future reflected-light searches using 4- and 8-m class telescopes.     

A SuperWASP search for additional transiting planets in 24 known systems

We present results from a search for additional transiting planets in 24 systems already known to contain a transiting planet. We model the transits due to the known planet in each system and subtract these models from light curves obtained with the SuperWASP (Wide Angle Search for Planets) survey instruments. These residual light curves are then searched for evidence of additional periodic transit events. Although we do not find any evidence for additional planets in any of the planetary systems studied, we are able to characterize our ability to find such planets by means of Monte Carlo simulations. Artificially generated transit signals corresponding to planets with a range of sizes and orbital periods were injected into the SuperWASP photometry and the resulting light curves searched for planets. As a result, the detection efficiency as a function of both the radius and orbital period of any second planet is calculated. We determine that there is a good (>50 per cent) chance of detecting additional, Saturn-sized planets in   P ∼  10 d orbits around planet-hosting stars that have several seasons of SuperWASP photometry. Additionally, we confirm previous evidence of the rotational stellar variability of WASP-10, and refine the period of rotation. We find that the period of the rotation is  11.91 ± 0.05  d, and the false alarm probability for this period is extremely low  (∼10⁻¹³)  .     

Propagation of local errors in the solutions of the differential equations for orbital elements

The propagation of errors in the solutions of the differential equations for the orbital elements of perturbed two-body motion is investigated. It is shown that the error in the time-element grows linearly for differential equations for orbital elements when only perturbations are present on the right-hand side, cubically for formulations which have a two-body term on the right-hand side, and linearly for formulations based upon extended phase space Hamiltonians.     

The full set of gas giant structures: I: On the origin of planetary masses and the planetary initial mass function

Context

Current planet search programs are detecting extrasolar planets at a rate of 60 planets per year. These planets show more diverse properties than was expected.

Aims

We try to get an overview of possible gas giant (proto-) planets for a full range of orbital periods and stellar masses. This allows the prediction of the full range of possible planetary properties which might be discovered in the near future.

Methods

We calculate the purely hydrostatic structure of the envelopes of proto-planets that are embedded in protoplanetary disks for all conceivable locations: combinations of different planetesimal accretion rates, host star masses, and orbital separations. At each location all hydrostatic equilibrium solutions to the planetary structure equations are determined by variation of core mass and pressure over many orders of magnitude. For each location we analyze the distribution of planetary masses.

Results

We get a wide spectrum of core-envelope structures. However, practically all calculated proto-planets are in the planetary mass range. Furthermore, the planet masses show a characteristic bimodal, sometimes trimodal, distribution. For the first time, we identify three physical processes that are responsible for the three characteristic planet masses: self-gravity in the Hill sphere, compact objects, and a region of very low adiabatic pressure gradient in the hydrogen equation of state. Using these processes, we can explain the dependence of the characteristic masses on the planet’s location: orbital period, host star mass, and planetesimal accretion rate (luminosity). The characteristic mass caused by the self-gravity effect at close proximity to the host star is typically one Neptune mass, thus producing the so-called hot Neptunes.

Conclusions

Our results suggest that hot Jupiters with orbital period less than 64 days (the exact location of the boundary depends on stellar type and accretion rate) have quite distinct properties which we expect to be reflected in a different mass distribution of these planets when compared to the “normal” planetary population. We use our theoretical survey to produce an upper mass limit for embedded planets: the maximum embedded equilibrium mass (MEEM). This naturally explains the lack of high mass planets between 3 and 64 days orbital period.     

Planetary orbital equations in externally-perturbed systems: position and velocity-dependent forces

The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss’ equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the “adiabatic” approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request.     

超短周期系外行星研究进展

超短周期(ultra-short-period,USP)行星是指轨道周期小于1 d的系外行星,是近年来系外行星研究领域中一个新的前沿目标。USP行星的搜寻与确认需要借助傅里叶变换(Fourier transform,FT)和盒最小二乘法(the box least,BLS)等光变曲线分析算法,以筛选和确认精准的周期信号。利用统计方法可得到目前USP行星的轨道周期、行星半径、宿主恒星类型等分布特征。大部分USP行星半径小于2R⊕,受行星质量限制,大多数USP行星无法通过视向速度信号测得精确的行星质量。根据已有的观测结果可算出,部分USP行星的质量小于10M⊕,由此推测这些USP的组成更接近金属与岩石混合的类地行星。由于密近轨道可能发生光致蒸发等物质损失过程,USP行星大气的存在情况尚不明确。目前,USP行星被认为起源于热木星(hot-Jupiters)或亚海王星(sub-Neptunes),但USP行星与热木星的主星金属丰度的分布存在较大差异,亚海王星的光致蒸发起源理论可能性更高。USP行星轨道演化机制包括低偏心率轨道迁移和潮汐耗散的原位起源模型等。     

Tidal evolution of close-in exoplanets in co-orbital configurations

In this paper, we study the behavior of a pair of co-orbital planets, both orbiting a central star on the same plane and undergoing tidal interactions. Our goal is to investigate final orbital configurations of the planets, initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting tidal evolution. The study is done in the form of purely numerical simulations of the exact equations of motions accounting for gravitational and tidal forces. The results obtained show that, at least for equal mass planets, the combined effects of the resonant and tidal interactions provoke the orbital instability of the system, often resulting in collision between the planets. We first discuss the case of two hot-super-Earth planets, whose orbital dynamics can be easily understood in the frame of our semi-analytical model of the 1/1 MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.